Probes for measuring resistivity in sheets and wafers are known in the art. One example of such probes is the four-point probe as shown in FIG. 1. The purpose of a 4-point probe is to measure the resistivity of a semiconductor material. It can measure either bulk or thin film specimens.
Referring to FIG. 1, there is shown a four-point resistivity probe 100. The probe 100 comprises four electrodes 110, 120, 130, and 140 for probing a wafer 150. In this example consider each of the electrodes to be equally spaced. The probe is placed in the interior of the sample, and the probes are collinear. Generally, the probe 100 works by applying a known level of current, I, between electrodes 110 and 140 via the wafer 150. Then the voltage, V, between electrodes 120 and 130 is measured. The resistance of the part of the wafer 150 being measured is determined using Ohm's law and the measured voltage V. Thus, V is divided by I to produce the sought resistance measurement. In this example, the polarity of current I or the voltage V could be the reverse of what is shown. In this case electrode 140 is a current source and electrode 110 collects the current while the voltage difference across electrodes 130 and 120 is measured. The current represented by arrow 160 actually flows throughout various paths in the wafer 150, defining a resistance network. The current 160 creates an electric field to be measured using a voltage meter. The resistance per square (R□) also referred to as “Rsq” is derived from these measurements according to well known relationships between the measured parameters. In the prior art it was known to make measurements using combinations of probes other than the one discussed but only one such combination was used to derive the resistance per square for a wafer. In the prior art more than one combination of probes was used when the probes were placed on the perimeter of the sample. Here we restrict ourselves to cases where the probes are placed in the interior of the sample.
As used herein, a “probe” is a device that is not affixed to the surface being measured. A probe can be affixed to an intermediate metal structure, such as a contact pad. Electric coupling of the probe to the tunnel junction film stack can occur through physical contact between the probe and the surface of the tunnel junction film stack, through a probe that is affixed to an intermediate metal structure, or through other techniques known to those skilled in the art.
Referring again to FIG. 1 there is shown an example of a device some researchers have used to measure resistance of tunnel junction films. A portion of a semiconductor wafer 150 to be measured is shown. The wafer 150 comprises a substrate 152 and an unprocessed stack 151 having a number of tunnel junction films. The tunnel junction films comprise the top layer 158, tunnel barrier 156, and bottom layer 154. The four-point probe 100 comprising probes 110, 120, 130, and 140, each separated by a distance, a, so that the entire distance from start to end of the four-point probe 100 is L. Each probe 110 through 140 contacts the top surface 162 of top layer 158. Probe 110 is used to inject current I, and probe 140 is used to collect the current after it passes through the unprocessed stack 151. Probes 120 and 130 are used to measure voltage V.
The four-point probe 100 is a well known tool used to characterize many different types of semiconductors and other materials. In fact, it is used to characterize Giant Magneto Resistive (GMR) films, which are used in read and write heads of many current hard drives. In GMR, the tunnel barrier 156 is replaced by a metal, which allows current to flow to the pinned layer 154. The four point probe 100 is also commonly used to measure the resistance of a blanket film. In this case the unprocessed stack 151 is composed of one or more conducting layers.
The resistance per square (R□), of the material of the wafer 150, is defined by the relationship R□=ρ/t, where ρ is the resistivity and t is the thickness of the material (wafer 150). Resistivity is a property of the material.
The method for measuring resistance or resistivity of wafer materials used by the apparatus of FIG. 1 works well for many purposes; however errors can occur in the resistivity measurements caused by the position of the probe points on the subject wafer or sheet.
Van der Pauw, “A Method for Measuring the Resistivity and Hall Coefficient on Lamellae of Arbitrary Shape,” 20 Philips Technical Review page 220 (1958), discussed a resistivity measurement of a flat lamella with four small contacts at arbitrary places on the periphery. However, the techniques discussed in that article only apply to measurements made on the periphery of the lamella measured
Therefore, there is a need for a resistance measurement system that overcomes these drawbacks in the known art.